A body of mass \( M \) at rest explodes into three pieces, in the ratio of masses 1:1:2. Two sma...

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A body of mass \( M \) at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of \( 30 \mathrm{~ms}^{-1} \) and \( 40 \mathrm{~ms}^{-1} \) respectively. The velocity of the third piece will be :
- (a) \( 15 \mathrm{~ms}^{-1} \)
(b) \( 25 \mathrm{~ms}^{-1} \)
(c) \( 35 \mathrm{~ms}^{-1} \)
(d) \( 50 \mathrm{~ms}^{-1} \)
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